I definitely get the gist I looked at what you sent period there's also one would a chocolate bar if you cut it a certain way after eating one piece you can make the entire bar again.. that's what I thought what you posted was akin to because I was going to actually say maybe the missing Square is borrowing a slight amount of area from each box..in other words if you had a undetectable stripe of one color edging all the other colors to make it vanishsays Surfcrab on Mar 30th 17 (#2533903)Reply | +1 | ♥1

There's an easy way to see that the lower figure contains an extra square cm.
In both cases, the entire colored figure is drawn on a 5 x 13 cm rectangle of area 65 sq cm.
If you work out the blank area OUTSIDE the first colored figure, you get 12 + 5 + 16 = 33 sq cm, so the figure itself must contain 65 - 33 = 32 sq cm.
Doing the same for the outside of the lower colored figure, you get 12 + 5 + 15 = 32 sq cm, so the figure itself must contain 65 - 32 = 33 sq cm, one more than in the first case.
http://data.amirite.net/user_im...91bcc7da9c.jpgsays Thinkerbell on Apr 20th 17 (#2550389)Reply | +1 | ♥1

The lower figure contains exactly the same amount of blue, red, green, and purple areas, it is just taking up more space because the colored areas were moved and one squares worth of uncolored space is now located inside the colored area, instead of outside.says Bozette on Apr 21st 17 (#2550470)Reply | +1 | ♥1

Yes, that happens because the (entire) colored area is not a true triangle in either case. The slope of the green triangle is a little steeper than that of the red one.
It is a packing problem. In the first case, the 32 colored squares pack together perfectly with no gaps to form the upper pseudo-triangle; In the second, the 32 colored squares pack together with one blank square left over. That's the 33rd square of the lower pseudo-triangle.says Thinkerbell on Apr 21st 17 (#2550481)Reply | 0 | ♥0

You didn't?
Gee, you only needed simple arithmetic to follow my solution. Just addition, subtraction and multiplication of integers.
The link's proof was so complicated, Thomas even had to leave out steps, in the interests of "sparing you the arithmetic" of adding and subtracting quantities raised to the fourth power and then taking the square root of the result, but I guess you did all that in your head. http://data.amirite.net/user_im...986a173e5d.jpgsays Thinkerbell on Apr 21st 17 (#2550601)Reply | 0 | ♥0

Simply counting the squares does not explain the why of the illusion.says Bozette on Apr 21st 17 (#2550859)Reply | +1 | ♥1

The why of the illusion was obvious from the beginning... the colored pseudo-triangle can't be a real triangle. The vertical and horizontal sides are straight, so the hypotenuse must be bent.
I'm talking about proving that the extra blank area is exactly 1 sq cm. The link used a sledge hammer to crack a peanut.
http://data.amirite.net/user_im...986a173e5d.jpg
I once had an algebra teacher that told us not to make problems more complicated than they needed to be. That was wise advice then, and remains so today.says Thinkerbell on Apr 21st 17 (#2550990)Reply | 0 | ♥0

Were it obvious to everyone, it wouldn't be a paradox, now would it?
I agree with your teacher and that the link went further into the math than was necessary. Your original statement, however, was an oversimplification that still didn't explain the paradox to those it was not obvious to.
Have a nice weekend, Thinkerbell.says Bozette on Apr 21st 17 (#2551139)Reply | 0 | ♥0

There are easily-resolved momentary paradoxes (like this "triangle" illusion) and there are also difficult paradoxes (such as those posed by quantum mechanics) that even the world's greatest physicists have not yet been able to resolve after 100 years.
Here is an old paradox, akin in some ways to the "triangle."
Three traveling salesmen, in order to save money, agree to share a room at a cheap hotel. The desk clerk tells them the overnight rate for the room is $30, and collects $10 from each salesman.
A short time later, the clerk realizes he made a mistake, that he should only have charged $25 for the particular room he gave the salesmen.
So the clerk gives the bellhop $5 in singles and sends him to the room with instructions to give the $5 to the salesmen.
But the bellhop is dishonest, giving only $3 to the salesmen ($1 to each), and keeping $2 for himself.
Now comes the question: Each salesman made a net payment of $9, or $27 total. The bellhop has $2. What happened to the remaining dollar of the original $30?says Thinkerbell on Apr 22nd 17 (#2551664)Reply | 0 | ♥0

The Omnipotent Paradox dates back to the 12th century to Averroës who asked, “Could an omnipotent being create a stone so heavy that even they could not lift it?” This would be like seeking an answer to the question, “What would happen if an irresistible force were to meet an immovable object?” This statement seems to make sense at first, but upon closer examination, we must ask if there is a force that is irresistible, and if there was, then there can be no immovable object. Both cannot be true because if an irresistible force does exist, then there cannot be an immovable object. The point is an object cannot in principle be immovable if a force exists that can in principle move it.
The answer is NO He cannot "do" that. Note that there is no limit however to the size of a rock that He can create, and there is no limit to the size of a rock that He can lift. Thus the question - answered in the negative - involves no limitation on God's prerogatives; if answered in the positive however does. The whole thing is a play on words.says Budwick on Mar 28th 17 (#2532198)Reply | +3 | ♥4

Yes but God could add material to the Rock and limit himself to how much material he can lift without wearing a safety harnesssays Surfcrab on Mar 30th 17 (#2533904)Reply | 0 | ♥0

Jokingly the point is we don't know if God has a limit to his own powers. When youman Ben's say he can do anything it might just pertain to what we consider anything no?says Surfcrab on Mar 30th 17 (#2533909)Reply | 0 | ♥0

A joking point?
You don't know about the power of God.
I don't know youman Ben or what he has said.says Budwick on Mar 30th 17 (#2533918)Reply | 0 | ♥0